Phase‐Transitions in White‐Dwarf Matter

Abstract

AbstractThe possibility of crystallization of white‐dwarf stars and neutron stars (very late stages of stellar evolution) was first pointed out by E. E. Salpeter (Astrophysic. J. 134, 669 (1961)) and A. A. A brikosov (Soviet Physics, JEPT 12, 1254 (1961)) and has become increasingly important since it can account for the existence of a double sequence of WD stars in the Hertzsprung‐Russel diagram (H. M. Van Horn, Astrophysic. J. 151, 227 (1968)) and for some models of pulsating stars (M. A. Ruderman, Nature 218, 1128 (1968)).Recent works on the subject (see in particular H. M. Van Horn: “Physical processes in white dwarf stars” in Kumar: “Low luminosity stars”, Gordon & Breach 1968) fail to determine the “melting” temperature of matter under conditions typical of the interior of such stars: an ion lattice (say 56Fe) embedded in a degenerate electron sea at densities of order 104‐107 g/cm3 and temperatures of order 105 ‐ 108 K. We have applied Tisza's theory of phase transitions to such a physical system to establish: 1. the order of the transition 2. the density‐temperature regions where crystallization may actually occur 3. to what extent the use “traditional” thermodynamics in dealing with such problems, is correct: in fact, according to modern statistical mechanics, the actual thermodynamic functions are obtained from the functions provided by statistical mechanics only after a suitable “thermodynamic limit” has been taken.